Mirror Surface Evaluation for the Einstein Telescope Using Virtual Mirror Maps

TL;DR

This paper presents a method combining metrology data and optical simulations to generate virtual mirror maps, aiding the design and evaluation of mirror surface quality for gravitational-wave detectors like the Einstein Telescope.

Contribution

It introduces a framework for creating realistic virtual mirror maps that incorporate measured surface distortions for use in optical performance simulations.

Findings

Virtual mirror maps accurately reproduce measured surface features.

Metrology-informed simulations help optimize mirror surface specifications.

The approach links surface quality requirements to existing detector performance.

Abstract

The performance of mirrors in optical interferometers is critically influenced by their surface quality. Accurate metrology enables mirror surfaces to be characterized through phase maps describing their three-dimensional structure after coating. In this work, we combine Zernike polynomial decomposition and spatial frequency (PSD) analysis with numerical optical simulations to quantify the impact of surface distortions on the reflected optical field. The method is validated using metrology data from mirrors currently installed in the Advanced Virgo gravitational-wave detector. Building on this validation, we introduce a framework for generating realistic virtual mirror maps that reproduce both low order aberrations and high spatial frequency content of measured surfaces. These virtual maps are used in optical simulations to systematically explore and compare candidate surface quality specifications for future detectors, with particular focus on the Einstein Telescope. Our results show that metrology-informed virtual mirrors provide a practical design tool to assess the impact of different surface specifications on optical performance, and to relate future requirements to the performance of existing interferometers.